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January 2007, Volume 100, Issue 5


President's Choice: Happy Integers
Mary Lindquist
The favorite article of a past NCTM president chosen for reprise as part of the celebration of the journal's 100th volume year. This article is about cheery sequences and happy numbers, with an opportunity to discuss wording of conjectures and to explore proofs. Includes a computer program in BASIC.

President's Choice: President's Report: Better Teaching, Better Mathematics: Are They Enough?
F. Crosswhite
The favorite article of a past NCTM president chosen for reprise as part of the celebration of the journal's 100th volume year. This article reports on the health of school mathematics education in the mid-1980's, right after the US Department of Education published What Works. SIMS reported our very best student did not compare well with their counterparts in other countries. Have we made any strides forward in the past 20 years to meeting the challenge laid out in the article?

Intersections of a Circle and a Square: An Investigation
Dan Canada, Stephen Blair
The investigation of how a circle and square lying in the same plane could intersect each other is an excellent example of geometric problem-solving. This paper explores three facets of the investigation: (1) finding out how many points of intersection are possible, (2) classifying the different ways of intersection, and (3) determining which ways are constructible, and how. Altogether, the investigation offers students and teachers alike a venue for exploring a rich task in geometry. Includes student work.

The Magic of Balanced Groups: Educational Applications of Magic Squares
Michael Bossé, N. Nandakumar, Melanie Ore
Provides students with many interesting observations regarding the nature of magic squares, magic rectangles, and quasi-magic squares and provides tools for teachers to group students into balanced cooperative learning groups.

Precision: The Neglected Part of the Measurement Standard
Donald Nowlin
The concepts of precision and significant digits are often ignored by mathematics teachers. The author examines the results of this trend and recommends five principles to use with problems involving measurements.

Professional Development for Mathematics Teachers: A Team Approach
P. Taylor, Brandy Ferrell, Terri Hopkins
Professional Development teams including in-service and preservice teachers offer a bridge across the continuum of mathematics teacher education. This manuscript documents the experience of one such team and reflections on the learning experience through the eyes of a member of the team at the preservice stage of her career as a teacher of mathematics.

Iterated Function Systems in the Classroom
Charles Waiveris
The title may appear daunting, but the exercises, which can be presented to students from middle school to graduate school, are not. The exercises center on creating fractal images in the xy-plane with free. easy-to-use software and questions appropriate to the level of the student. Numerous images are shown.

Helping Students Make Sense of Mathematics
Wendy Sanchez
Specific strategies for focusing lessons on helping students develop a conceptual understanding of mathematics. Teaching that focuses on why mathematical procedures work rather than merely on how to do procedures can help students make sense of mathematics.